The Law of non-contradiction might be the most obvious law of logic. It simply states that A cannot be both A and non-A at the same time in the same respect. This means that a statement cannot be both true and false simultaneously and in the same way.
This law in application means that two statements cannot contradict each other and both be true. For example, I could say that a ball is completely black, and you could say that the ball is completely white. One of us must be wrong. According to the law of non-contradiction the ball cannot be both A (black) and non-A (white) at the same time and in the same respect.
Using this law of non-contradiction can prove to be helpful when addressing religious pluralism, the belief that all religions are equally valid and true.
For instance, Christians say that Jesus is the Son of God.
Muslims say that Jesus was not the Son of God, but a prophet.
Jews would say that Jesus was just a man.
Some Hindus might say that Jesus was an avatar (incarnation) of Vishnu, or that he was God, but God in the sense that all things are divine.
These religions clearly contradict each other on the historical person of Jesus Christ. Jesus cannot be A (God) and non-A (not God) at the same time in the same respect. According to the law of non-Contradiction, religious pluralism commits a logical fallacy, either that it is an intolerant position which denies each religion of true teachings and uniqueness or it is an ignorant position only made by those who have not taken the time to study the world's religions.
The following video shows this apologetic put into practice:
A world of Difference by Kenneth Richard Samples contains a chapter entitled Logic 101 and Christian Truth-Claims, which might prove as a helpful read if you want to know more on this subject.